This paper studies the off-line wavelength assignment problem in star and ring networks that deploy multiple fibers between nodes and use Wavelength Division Multiplexing (WDM) for transmission. The results in this paper show that the ability to switch between fibers increases wavelength utilization. In particular, sharper per-fiber bounds on the number of required wavelengths are derived for the multifiber version of the assignment problem in star and ring networks. Additionally, the complexity of the problem is studied and several constrained versions of the problem are also considered for star and ring networks. A summary of contributions is provided in the first section. 1 Introduction Optical networks hold out the promise of meeting the high transmission quality and large bandwidth desired by end-user applications. Among various transmission technologies for optical networks, Wavelength Division Multiplexing (WDM), because of its efficient use of bandwidth, has received consider...

This paper studies the problem of All-to-All Communication for optical networks. In such networks the vast bandwidth available is utilized through wavelength division multiplexing (WDM): a single physical optical link can carry several logical signals, provided that they are transmitted on different wavelengths. In this paper we consider all-optical (or singlehop) networks, where the information, once transmitted as light, reaches its destination without being converted to electronic form in between, thus reaching high data transmission rates. In this model, we give optimal all-to-all protocols, using minimum numbers of wavelengths, for particular networks of practical interest, namely the d-dimensional square tori with even side, the corresponding meshes and the Cartesian sums of complete graphs.

We study the problem of centrally scheduling multiple messages in a linear network, when each message has both a release time and a deadline. We show that the problem of transmitting optimally many messages is NP-hard, both when messages may be buffered in transit and when they may not be; for either case, we present efficient algorithms that produce approximately optimal schedules. In particular, our bufferless scheduling algorithm achieves throughput that is within a factor of two of optimal. We show that buffering can improve throughput in general by a logarithmic factor (but no more), but that in several significant special cases, such as when all messages can be released immediately, buffering can help by only a small constant factor. Finally, we show how to convert our centralized, offline bufferless schedules to equally productive fully...

Abstract In this paper we study wavelength assignment on an optical linesystem without wavelength conversion. Consider a set of undirected demands along the line. Each demand is carried on a wavelength and any two overlapping demands require distinct wavelengths. Suppose _ wavelengths are available in the system. We define `(e), the load on link e, to be the smallest integer such that `(e) _ is at least the number of demands passing through e. Hence, `(e) is the minimum number of fibers required on e in order to support all demands. We present a polynomial-time wavelength assignment algorithm that guarantees each wavelength appears at most `(e) times on each link e. (This generalizes the well-known fact that interval graphs are perfect.) In the presence of MOADMs (mesh optical add/drop multiplexers), devices that multiplex distinct wavelengths from different fibers into a new fiber, we only need to deploy `(e) fibers per link. On the other hand, if each demand has to stay on a single fiber, as is the case without MOADMs, we show that some links may require more than `(e) fibers. In fact, we show that it is NPcomplete to decide if a set of demands can be carried on a given set of fibers, or if there exists a set of fibers with a given total length that can carry all the demands.

This paper proposes algorithms for allocation of wavelengths to connections (lightpaths) in optical wavelength division multiplexed networks, predominantly for ring topologies. The worst-case situation is considered where no blocking is allowed, and there are no assumptions on the traffic arrival and holding times. The traffic is characterized only by its load L, which is the maximum number of lightpaths that can be present on any link assuming no blocking.

Modern high-performance communication networks pose a number of challenging problems concerning the efficient allocation of resources to connection requests. In all-optical networks with wavelength-division multiplexing, connection requests must be assigned paths and colors (wavelengths) such that intersecting paths receive different colors, and the goal is to minimize the number of colors used. This path coloring problem is proved NP-hard for undirected and bidirected ring networks. Path coloring in undirected tree networks is shown to be equivalent to edge coloring of multigraphs, which implies a polynomial-time optimal algorithm for trees of constant degree as well as NP-hardness and an approximation algorithm with absolute approximation ratio 4:3 and asymptotic approximation ratio 1:1 for trees of arbitrary degree. For bidirected trees, path coloring is shown to be NP-hard even in the binary case. A polynomial-time optimal algorithm is given for path coloring in undirected or bidir...

We consider the maximum disjoint paths problem and its generalization, the call control problem, in the on-line setting. In the maximum disjoint paths problem, we are given a sequence of connection requests for some communication network. Each request consists of a pair of nodes, that wish to communicate over a path in the network. The request has to be immediately connected or rejected, and the goal is to maximize the number of connected pairs, such that no two paths share an edge. In the call control problem, each request has an additional bandwidth speci cation, and the goal is to maximize the total bandwidth of the connected pairs (throughput), while satisfying the bandwidth constraints (assuming each edge has unit capacity). These classical problems are central in routing and admission control in high speed networks and in optical networks.

In this paper, we consider the traffic grooming, routing, and wavelength assignment (GRWA) problem for optical mesh networks. In most previous studies on optical mesh networks, traffic demands are usually assumed to be wavelength demands, in which case no traffic grooming is needed. In practice, optical networks are typically required to carry a large number of lower rate (sub-wavelength) traffic demands. Hence, the issue of traffic grooming becomes very important since it can significantly impact the overall network cost. In our study, we consider traffic grooming in combination with traffic routing and wavelength assignment. Our objective is to minimize the total number of transponders required in the network. We first formulate the GRWA problem as an integer linear programming (ILP) problem. Unfortunately, for large networks it is computationally infeasible to solve the ILP problem. Therefore, we propose a decomposition method that divides the GRWA problem into two smaller problems: the traffic grooming and routing problem and the wavelength assignment problem, which can then be solved much more efficiently. In general, the decomposition method only produces an approximate solution for the GRWA problem. However, we also provide some sufficient condition under which the decomposition method gives an optimal solution. Finally, some numerical results are provided to demonstrate the efficiency of our method.

A new measure, the accommodating function, for the quality of on-line algorithms is presented. The accommodating function, which is a generalization of both the competitive ratio and the accommodating ratio, measures the quality of an on-line algorithm as a function of the resources that would be sufficient for an optimal algorithm to fully grant all requests. More precisely, if we have some amount of resources n, the function value at ff is the usual ratio (still on some fixed amount of resources n), except that input sequences are restricted to those where all requests could have been fully granted by an optimal algorithm if it had had the amount of resources ffn. The accommodating functions for three specific on-line problems are investigated: a variant of bin-packing in which the goal is to maximize the number of objects put in n bins, the seat reservation problem, and the problem of optimizing total flow time when preemption is allowed.

SONET (Synchronous Optical NETworks) add-drop multiplexers (ADMs) are the dominant cost factor in the WDM(Wavelength Division Multiplexing)/SONET rings. The number of SONET ADMs required by a set of traffic streams is determined by the routing and wavelength assignment of the traffic streams. Previous works took as input the traffic streams with routings given a priori and developed various heuristics for wavelength assignment to minimize the SONET ADM costs. This paper contributes mainly in two aspects. First, in addition to the traffic streams with pre-specified routing, this paper also studies minimizing the ADM requirement by traffic streams without given routings, a problem which is shown to be NP-hard. Second, new heuristic are proposed and analyzed for both the prespecified routing and the non-prespecified routing versions. The Preprocessed Iterative Matching heuristic has approximation ratio in between 4/3 and 3/2. A local-improvement algorithm has approximation ratio exactly 3...